Related to and integral with the discussion on quantity are the important knowledge and background on the types of wastewater, sources of water and wastewater, and methods of population projection. The various categories of quantities in the form of design flow rates are also very important. These topics are discussed in this chapter. Because of various factors that have influenced the rate of wastewater generation in recent times, including water conservation and the expanded use of onsite systems, it is critical that designers have more than just typical wastewater generation statistics to project future usage. Thus, a method of determining accurate design flow rates calculated through use of probability concepts are also discussed in this chapter. This method is called probability distribution analysis; it is used in the determination of the quantities of water and wastewater, so it will be discussed first.

Figure 1.1 shows a typical daily variation for municipal sewage, indicating two maxima and two minima during the day. Discharge flows of industrial wastewaters will also show variability; they are, in general, extremely variable and "explosive" in nature, however. They can show variation by the hour, day, or even by the minute. Despite these seemingly uncorrelated variability of flows from municipal and industrial wastewaters, some form of pattern will emerge. For municipal wastewaters, these patterns are well-behaved. For industrial discharges, these patterns are constituted with erratic behavior, but they are patterns nonetheless and are amenable to analysis.

Observe Figure 1.2. This figure definitely shows some form of pattern, but is not of such a character that meaningful values can be obtained directly for design purposes. If enough data of this pattern is available, however, they may be subjected to a statistical analysis to predict design values, or probability distribution analysis, which uses the tools of probability. Only two rules of probability apply to our present problem: the addition rule and the multiplication rule.

1.1.1 Addition and Multiplication Rules of Probability

Before proceeding with the discussion of these rules, we must define the terms events, favorable event, and events not favorable to another event. An event is an occurrence, or a happening. For example, consider Figure 1.3, which defines Z as "Going from A to B." As shown, if the traveler goes through path E, he or she arrives at the destination point B. The arrival at B is an event. The travel through path E that causes event Z to occur is also an event.

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